Question

Solve right triangle ABC with C=40 A=31.9 degrees c=23.8 ft

Answer 1

B =
`108.1^(o)`

a = 19.6 ft

b = 31.2 ft

To solve the given triangle, we apply the sine rule. The sine rule states that:

`(a)/(sin A)` =
`(b)/(sin B)` =
`(c)/(sin C)`

But,

A + B + C = 180

31.9 + B + 40 = 180

B = 180 - 71.9

= 108.1

B =
`108.1^(o)`

`(a)/(sin A)` =
`(c)/(sin C)`

`(a)/(sin 31.9^(o) )` =
`(23.8)/(sin 40)`

a = 19.57

a = 19.6 ft

Also,

`(b)/(sin B)` =
`(c)/(sin C)`

`(b)/(sin 108.1^(o) )` =
`(23.8)/(sin 40)`

b = 35.19

b = 35.2 ft